An effective seal must be provided between the valve body; and the rotary slide of such a valve, associated with each of the ducts provided in the body, to allow the passage of the fluid and can have means capable of making a tight contact with the rotary slide. The devices with which the invention is concerned are those having an annular gasket pressed against the rotary slide by the hydrostatic pressure of the fluid. In known devices of this type the gasket is part of an assembly movable by the fluid pressure and having generally the shape of an annular piston located around the corresponding duct. This construction is cumbersome and difficult to use for small-section valves. In addition, the movements of the rigid assembly are affected by friction so that the force applied to press the sealing gasket against the rotary slide is not entirely proportional to the hydrostatic pressure and leaks can occur.